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2021 JMPSC Invitationals Problems/Problem 4

Revision as of 14:01, 11 July 2021 by Samrocksnature (talk | contribs) (Created page with "==Problem== Let <math>(x_n)_{n\geq 0}</math> and <math>(y_n)_{n\geq 0}</math> be sequences of real numbers such that <math>x_0 = 3</math>, <math>y_0 = 1</math>, and, for all...")
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Problem

Let $(x_n)_{n\geq 0}$ and $(y_n)_{n\geq 0}$ be sequences of real numbers such that $x_0 = 3$, $y_0 = 1$, and, for all positive integers $n$, \begin{align*} x_{n+1}+y_{n+1} &= 2x_n + 2y_n,\\ x_{n+1}-y_{n+1}&=3x_n-3y_n. \end{align*} Find $x_5$.

Solution

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